Possible Insight

Climate Change Tail Risk

In my previous three posts (1, 2, 3), I argued that the optimal response to climate change—given our best evidence, economic theory, and a low social discount rate—is a tax and subsidy regime using a social cost of carbon of $29 per metric ton.

This policy optimizes the average outcome. But we should also consider the risk of very bad outcomes. Relevant terms of art include: tail risk, catastrophic risk, existential risk, asymmetric damage function, and the Precautionary Principle.

As it happens, I know a fair bit about this topic. I studied it in graduate school, I researched it extensively in the late 2000s, and then started an investment firm focused on startup tail risk. I’ve spent countless hours in front of the computer modeling this kind of risk.

Tail risk is a very complicated topic. I have tried to exercise a corresponding amount of caution in my approach and conclusions. But I also don’t want overconfience on the other side of the argument leading to ill-advised policies. With that said, I will present my perspective on climate change tail risk in three parts, ending as usual with some final thoughts:

  • The basic principles that must apply to climate tail risk.
  • An assessment of the evidence on climate tail risk.
  • The proper form of a discussion on mitigating climate tail risk

Basic Principles

To illustrate what I consider basic principles of tail risk, I’ll open with a quote that violates them.

… high quantities of any pollutant put us at a rapidly increasing risk of destabilizing the climate, a system that is integral to the biosphere. Ergo, we should build down CO2 emissions, even regardless of what climate models tell us.

…This leads to the following asymmetry in climate policy. The scale of the effect must be demonstrated to be large enough to have impact. Once this is shown, and it has been, the burden of proof of absence of harm is on those who would deny it.

Nasim Taleb, Climate models and precautionary measures.

This quote is not a strawman. Nassim Taleb is an expert on tail risk. I have tremendous respect for Taleb. His book, The Black Swan, was a revelation. It clarified many deep issues that had troubled me over the years and was the initial inspiration for my investment firm’s strategy.

But he is badly mistaken here. Notice first also how he simply assumes that the climate can be destabilized by pollutants in the quantities that humans are actually emitting. He doesn’t even consider the data we have on this topic.

Even stipulating to this premise, there are several obvious issues:

  • Budget constraints matter. What if addressing all the risks that meet this test exceeds our ability to pay?
  • Relative risk matters. If faced with more than one such risk, shouldn’t we address the most dangerous one first?
  • Probability matters. Isn’t there a big difference between risks that have a 1 in 1M vs 1 in 100 chance of occurring?
  • Costs matter. Isn’t there a big difference between risks that require 0.01% of world economic output to reduce vs 10%.
  • Moral tradeoffs really matter. Isn’t it a difficult moral question if substantially reducing a risk would cause people to definitely die in the near future in order to potentially save people from dying in the far future?

The rest of this section addresses each issue in detail.

Budget Constraints

Taleb’s argues that certain actions may destabilize the complex systems on which civilization depends and therefore the default should be to avoid those actions unless they can be proven safe to some level of certainty. In the case of CO2, this rule means reducing—presumably significantly—the rate of emissions

My first question is: how much does he think we need to reduce CO2 tail risk? I’m not asking for a precise probability; a rough factor of two will do. Do we need to reduce it to half? To a quarter? An eighth?

Whatever the target level, it logically implies we must also address any other risk that is at least as great as that target. For example, let’s say Taleb feels we should reduce CO2 tail risk by roughly a factor of 8. But say there are also three other tail risks (such as nuclear war, bioterrorism, and asteroid impacts) with a probability that is roughly 1/4 that of CO2. Clearly, once we reduce CO2 risk to 1/4, pushing it from 1/4 to 1/8 doesn’t make sense if we leave the four other tail risks at 1/4.

As we push CO2 risk lower, we “collect” other sources of risk that we must also address to achieve the lowest total risk. But can we afford this level of risk reduction? Global GDP is roughly $90T. That sounds like a huge budget. But most of that just goes toward keeping civilization up and running—food, shelter, medicine, education, transportation, and infrastructure. What we might call our “discretionary” GDP is much smaller. Our catastrophic risk budget is perhaps at most a few percentage points of the total.

Now that’s still on the order of trillions dollars per year. We can afford some risk reduction. But contra Taleb, we can’t just go ahead spend it on a particular source of risk without making some calculations. Notice that I haven’t “denied” anything here. I agree that we should consider reducing catastrophic risks. I agree that CO2 emissions might constitute such a risk. But this situation does not logically imply that we do whatever it takes to reduce CO2 emissions.

Relative Risk

“Collecting” other tail risks as we push CO2 risk down assumes that it’s the greatest risk. But what if there are even greater risks? If there’s a tail risk that is more likely, would have greater impact, and costs less to reduce, then it “dominates” CO2 risk. Again, as a matter of logic, we need to reduce that risk to the point where it no longer dominates before we allocate any resources to CO2 risk.

There are people who think seriously about these issues. Nick Bostrom is reasonably famous for his categorization of existential risk. Depending on what you consider plausible, there are roughly one to two dozen significant known categories of existential risk, including runaway global warming.

Importantly, two of the other risks Bostrom identifies are: “misguided world government or another static social equilibrium stops technological progress” and “repressive totalitarian global regime”. Plausibly, a draconian worldwide CO2 reduction effort would increase these risks. So even within existential risk, there might be a tradeoff in how strong of a CO2 policy we should adopt.

Notice how this dynamic creates a conflict within Taleb’s rule—CO2 emissions could plausibly present an existential risk from runaway global warming so we should default to strong action against CO2 emissions, but strong action against CO2 emissions could plausibly present an existential risk from a misguided or totalitarian government, so we should default to not taking strong action against CO2 emissions. I’m not saying we know whether the risk of one is greater than the other. Rather, I’m pointing out that we can’t simply default to one course of action as Taleb suggests.

We must consider the relative risk level from different sources. Applying overly simplistic decision rules to each source in isolation can bankrupt our budget or leave us exposed to greater overall risk than necessary.


Taleb asserts that the “scale of the effect” is what triggers his preferred default policy. So we should treat a 1 in 100 risk the same as 1 in 1M? 1 in 1B? Put another way, if we faced one 1 in 100 risk and four 1 in 10K risks, all with roughly the same impact, should we allocate the same amount of effort to reduce each one?

From reading Taleb’s work, I am quite aware that it’s difficult to estimate the precise probability of tail events, even with multiple observed datapoints. But surely we can try to get within a couple orders of magnitude.

My point here is not that climate tail risk doesn’t warrant some action. Rather, my point is that we can’t simply ignore the probabilities, rough estimates though they may be. We must still allocate scarce resources among different policy alternatives. So we need an estimate for the probability of climate catastrophe that properly weights the evidence.


The flip side of probability is the cost to reduce the risk. According to Taleb’s policy, should we simply default to incurring the costs, regardless of whether they are 1/1M, 1/1K, or 1/10th of our resources?

Moreover, this policy makes no mention of effectiveness. So we’re supposed to treat reductions of 1/2, 1/4, and 1/8 the same?

Obviously, combining these two objections gives us the challenge of cost-effectiveness. Surely there’s a difference between risks where it would cost very little to achieve very large risk reductions and those where it would be very expensive to achieve very modest risk reductions. But Taleb’s rule does not distinguish between the two.

Again, I am not saying we shouldn’t spend resources addressing climate tail risk. I’m saying we need to make some effort to assess the costs and benefits. If there is a significant probability of climate catastrophe, we need an estimate of how much it costs to reduce that probability a given amount, again, based on appropriate evidence.

Moral Tradeoffs

Human lives are a cost deserving special treatment. What if an activity saves tens of millions of lives per year, but creates a significant level of pollution. There’s some probability that this pollution could eventually lead to environmental damage that kills hundreds of millions of people per year in the future. Per Taleb, do we simply default to letting the tens of millions per year die now?

What if a doctor in a war torn country had a dying child in front of her? She could save the child, but only by consuming time and resources that might let ten other children die. Should she let the child in front of her die?

Notice that these two dilemmas are roughly parallel. So you should probably say either yes or no to both.

The Trolley Problem is a famous thought experiment in ethics designed to explore trading off few lives for many. People’s moral intuitions in these situations are extremely sensitive to how the problem is structured and worded. They don’t appear consistent across different variations. When you throw uncertainty about how many people will be saved and/or sacrificed, you get further inconsistencies, as famously demonstrated in Tversky and Kahneman’s “Asian Disease” paper.

I don’t claim to have the correct answers to these types of moral dilemmas. However, the fact that they remain dilemmas further argues against simple decision rules like Taleb’s.

Danger in Both Directions

Beyond these counters to Taleb, I want to stress another important principle of climate tail risk. There is no purely precautionary path.

Many people just assume that reducing CO2 emissions is “safe”. But CO2 emissions are a byproduct of using fossil fuels for energy. Reducing them requires reducing energy from fossil fuels. Such a reduction is not necessarily safe as the following graphics from Our World in Data illustrate.

Until the mid-1800s, most people lived at a subsistence level of poverty—with all the suffering and dying that entails. The Industrial Revolution enabled an increasing fraction to move beyond that level, eventually achieving an absolute reduction in the number of people living in poverty around 2000.

Increasing energy consumption accompanied this improvement. It seems pretty reasonable to infer a causal link between energy use and reduced poverty given that energy is a necessary ingredient for the complex industrial base that can support a large population. Clearly, fossil fuels have historically provided most of the required energy since escaping mere subsistence.

As the last graphic shows, even today, fossil fuels provide most of our energy. According to BP’s 2019 Statistical Review of World Energy, renewables made up just 4.0% of worldwide primary energy consumption in 2018. Nuclear accounted for another 4.4% and hydroelectric 6.8%. So fossil fuels currently make up about 85% of primary energy consumption.

What do you think would happen if the major world powers suddenly agreed to enforce a total ban on fossil fuel use? I’m pretty sure civilization would collapse almost immediately. In fact, I’m quite certain the probability of collapse is substantially higher than the probability a climate catastrophe would wipe out civilization if fossil fuel use continues on the current trajectory.

Of course, proponents of strong climate action will undoubtedly respond, “We’re not advocating the immediate abolishment of fossil fuels.” You’re not? Great! Then let’s have a sincere, scientific discussion about the tradeoffs at different levels and schedules for reduction.

One thing we can be pretty sure of is that any policy aimed at reducing fossil fuel use will raise energy prices and thereby kill people. How many? I’m not sure. I looked and couldn’t find any studies directly on point. It seems like a glaring oversight that, in the rush to estimate impacts of climate change, nobody allocated resources to assess the side effects of policies designed to combat it.

However, we do know that higher energy prices would likely kill people. The use of non-modern fuel sources causes millions of death per year. Obviously, making modern fuel sources more expensive is going to slow the rate at which poor countries transition and thereby increase the number of expected deaths vs faster industrialization. Moreover, even in advanced industrial countries, people die from energy poverty

More on point, a recent working paper estimated the increase in mortality caused by increases in electricity prices following the Fukishima nuclear accident. Nuclear power production, which accounted for over 30% of total production, halted across Japan. Electricity prices rose up to 38%. The authors estimate that this increase caused 1,280 deaths from 2011-2014 in Japan’s 21 largest cities (combined population of 35.2M). These excess deaths occurred in a rich, highly industrialized country. The effect would probably have been much more severe in a typical developing country.

I’m not saying that there is no justification for action. Remember that I advocate a carbon tax that will increase energy prices—I fully realize this policy will inevitably lead to some specific deaths that would not have otherwise occurred. But these deaths are part of a careful cost-benefit analysis. Given that people’s lives are at stake, I feel pretty strongly we should weigh the options carefully rather than simply declaring one path “cautious” and ignoring the deaths in that column.

How Big Is Climate Tail Risk?

Now for the trillion dollar question… what is the ballpark estimate of the probability a CO2-driven climate catastrophe occurs within the next century or so? It would be impossible to understate just how difficult this question is. Anyone who claims to have nice neat answer is most likely mistaken.

We can’t rely on estimates from climate models. As I showed in the first two posts of this series, models can’t reproduce near-past or present temperatures very well, can’t predict near-future temperatures very well, and disagree in their estimates of CO2 sensitivity with the overall literature. Because errors in complex systems usually compound, extrapolating models that work poorly in known regimes to extreme regimes is unlikely to produce sensible results.

Now, this isn’t to say that the models couldn’t improve. As I suggested in my original post, I think if climate modelers worked with experts from other fields, the chance are good they would get better short- to medium-term forecasts. It’s certainly possible that these models could also produce longer term forecasts that have implications verifiable today. Perhaps something that would appear in the geologic record from a time with similar conditions. But until then, I don’t see any justification for treating GCM runs with more extreme levels of CO2 as anything more than hypotheses.

We probably can’t rely on expert judgement either. In my graduate program, we used probabilities elicited from experts to help calculate optimal decisions. In practice, it was extremely challenging to extract coherent values. When I went over to the psychologically department to see what Amos Tversky had to say on the subject, I learned why.

Humans brains just don’t do probabilities very well. Yes, if you use a very structured elicitation protocol on multiple experts with routine experience of the target outcomes, you can do pretty well at making coarse distinctions among probabilities between 10 and 90 percent. But once you have to deal with somewhat extreme probabilities or outcomes outside their direct experience, you simply can’t rely on them,

This relatively recent AER article, reviews the situation. When people estimate rare events from descriptions of the outcome scenario, they both overestimate the probability and overweight the consequences. For climate tail risk, the publication bias in top journals towards more extreme results is likely to exacerbate this effect due to availability bias. I suppose it’s possible that someone could devise an expert probability assessment protocol that demonstrates reasonable calibration to verifiable climate outcomes. In that case, we could have some confidence in them as applied to catastrophic scenarios. But as far as I know, we do not currently have such a tool.

What’s left? Well, we do have a fair amount of long term geologic data about temperature, CO2, and life on Earth. What does this evidence say about CO2-driven climate catastrophes? First, let’s orient ourselves with a graph of reconstructed temperatures and CO2 levels over the last 450 million years.

In general, both CO2 and temperature have been significantly higher since the time of dinosaurs. Based on this record, we do not currently seem to be near an upper CO2 or temperature threshold that would inherently make the Earth uninhabitable by humans. So there is little reason to assume a priori that a few hundred ppm of CO2 will tip us into a dangerous temperature regime (the scale on the vertical axis is thousands of ppm).

Of course, it’s possible there are specific conditions under which a relatively modest but rapid rise in CO2 could be harmful to animal life. To assess this risk, we can look to geologic and paleontologic evidence of conditions that have killed large swaths of animal life.

In terms of historic extinction events, as far as I can tell, Norman MacLeod was one of the world’s top experts. He has a well known book, The Great Extinctions, and published many relevant papers. When he examined extinction events over the last 600 million years, the most statistically associated causes are volcanic eruptions and sea level drops (due to glaciation), with asteroid impact a distant third.

There is some speculation based on models that CO2 may have caused runaway warming during the Permian-Triassic mass extinction, though from volcanic eruptions, which produce a variety of effects in addition to CO2. The paper is very recent and pay-walled. And, as seems pretty clear, models could at most be suggestive under these circumstances.

[UPDATE 12/6/2019: a reader sent me the paper. I had to go to the supplementary materials, but here’s what’s happening:

  • They initialize the model with a 2000 year run of CO2 at 150ppm.  This is weird because the references I’ve seen show CO2 levels over 1000pm for at least the last 10M years of the Permian.  (For example: this paper.)
  • Then they model an instantaneous increase to 5580ppm (yes, five thousand) and sustain it for 3000 years.
  • They then consider as confirmatory evidence the pattern of extinction by latitude.  But the mechanism is simply O2 concentration drops in the ocean due to the temperature change itself. As far as I can tell, anything that raised the temperature 11 deg C would cause the same pattern.

So not a very compelling argument in terms of parallels to today.]

In terms of consensus on the causes of that particular extinction, the world’s expert is Douglas Erwin, curator in the Department of Paleobiology at the Smithsonian’s National Museum of Natural History. He has the definitive book on the topic and the freely available introduction makes clear that he does no think global warming is one of the candidate causes. Moreover, when this event occurred 252 million years ago, CO2 levels were roughly 5X their current levels, making the parallel even more tenuous.

So when we look at specific causes of previous threats to animal life on Earth, there is no evidence that changes in CO2 within the ranges we’re likely to experience have been a major factor. Obviously, this does not preclude such possibility. However, it certainly indicates that runaway warming from CO2 emissions is unlikely to be the biggest long term threat. Volcanic eruptions, glaciation, and asteroid impacts appear more significant. To those, I would add the human-generated threat of conflicts involving weapons of mass destruction. As I argued above, the logic of catastrophic risk means we must take into account the relative probabilities and effectiveness of reduction alternatives.

Thinking About Mitigation

Again, I am not saying that the possibility of global warming catastrophe isn’t worth some consideration. I’m simply saying there’s no strong evidence that it’s a dire immediate threat. We can afford to perform some careful analysis.

The best way to frame the question is in terms of insurance: how big is the risk, how much does a policy cost, and how much coverage does it provide. If you have a 1 in 100 risk of complete loss that costs 1/10,000th of your bankroll to fully insure, that may be a good deal (depending on how many total 1 in 100 risks you face—if you face 100s of them, you can’t even afford that). If it costs 1/10th? Not so much. Also questionable if it costs 1/100th to reduce the risk by only 10%, to 9/1000.

So how much does an insurance policy cost to reduce our catastrophic climate risk by a certain amount? I have no idea. I looked pretty hard and can’t seem to find any source that both frames the issue in terms of insurance against catastrophe and has plausible numeric estimates.

It does appear that the cost would be substantial. The IPCC thinks that a 1.5 deg C limit is desirable in general. That limit is the entire focus of its 2018 special report. On page 95 of Chapter 2, it states achieving this limit will cost 3-4X achieving a 2.0 deg C limit.  Now, that report uses climate sensitivities from models that I’ve shown may be too high, but the calculations of the required reductions in fossil fuel use clearly indicate the marginal financial cost of limiting CO2 emissions increases pretty steeply in the range we care about.

What I’d like to see is an accounting that sounds at least vaguely like, “We can reduce the chance of a catastrophe that would cause X deaths and a Y% reduction in world GDP for Z years from A% to B% by spending $C and incurring D deaths.” Where these numbers are all very rough estimates. From an ethical perspective, I don’t think we should simply buy this insurance without some handle on these variables—because there is a significant cost of this insurance in lives.

Even in the absence of such an accounting, there are likely some modest hedges worth making. R&D dollars or prizes for lower- or no-carbon energy solutions seems worthwhile. If we can develop such systems that deliver similar cost, reliability, and portability to fossil fuel options, even if only in a subset of applications, that’s likely a worthwhile investment. But as I showed in a previous post, production subsidies and mandates tend not to be cost effective. Similarly R&D dollars or prizes for carbon capture and geoengineering solutions with minimal side effects are likely advisable. If it turns out that we get new data raising the estimated probability of CO2-driven climate catastrophe, having the option to more quickly deploy cooling solutions would be valuable. However, aggressive measures targeted at fossil fuel use do not currently appear justified.

Final Thoughts

  • As in my original cost-benefit analysis, there is a tradeoff. Fossil fuels provide cheap, reliable, and portable energy. Reducing climate change tail risk currently requires foregoing these benefits to some extent.
  • Reducing fossil fuel use costs lives as well as dollars.
  • There is no simple decision rule that effectively determines how much we should reduce fossil fuel use to reduce climate change tail risk.
  • We must take into account our overall tail risk budget, relative risk of climate tail outcomes, and cost effectiveness of reduction measures.
  • Neither climate models nor geologic data currently provide strong evidence that climate change presents a large, immediate tail risk. Other people may disagree with this final conclusion. But it is backed up by data and shouldn’t be dismissed out of hand.


Written by Kevin

November 29, 2019 at 10:20 pm

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